Blender noise during paint in Texture paint mode
In texture painting, brush can have a texture assigned to it as a pattern. When it is, the pattern will be applied to every stroke done with the brush (appearence will depend on settings of the brush mapping etc.):



See more about how to assign a texture to the brush and paint with it.

If you want to continue drawing with solid color, unlink that texture in brush settings by pressing X button next to its name. For more about that refer to Users (Sharing) and Removing data-blocks in manual.